摘要翻译:
本文利用混沌系数的多项式-指数参数化方法,将利率混沌模型与市场数据进行标定。我们确定了一类单变量模型,它允许我们以受控的方式从高阶混沌中引入复杂性,同时保持相当的分析可处理性。特别地,我们根据正态密度和累积分布函数的初等组合,导出了一变量三级混沌模型中债券和期权价格的显式表达式。然后,我们将混沌模型的校准性能与已知的基准模型进行了比较。对于期限结构的校正,我们发现混沌模型可以与Svensson模型相媲美,其优点是保证正性,并与利率的动态随机演化相一致。对于期权数据的校准,混沌模型优于Hull和White以及rational对数正态模型,并与LIBOR市场模型相当。
---
英文标题:
《Calibration of Chaotic Models for Interest Rates》
---
作者:
Matheus R Grasselli and Tsunehiro Tsujimoto
---
最新提交年份:
2011
---
分类信息:
一级分类:Quantitative Finance 数量金融学
二级分类:Pricing of Securities 证券定价
分类描述:Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
--
---
英文摘要:
In this paper we calibrate chaotic models for interest rates to market data using a polynomial-exponential parametrization for the chaos coefficients. We identify a subclass of one-variable models that allow us to introduce complexity from higher order chaos in a controlled way while retaining considerable analytic tractability. In particular we derive explicit expressions for bond and option prices in a one-variable third chaos model in terms of elementary combinations of normal density and cumulative distribution functions. We then compare the calibration performance of chaos models with that of well-known benchmark models. For term structure calibration we find that chaos models are comparable to the Svensson model, with the advantage of guaranteed positivity and consistency with a dynamic stochastic evolution of interest rates. For calibration to option data, chaos models outperform the Hull and White and rational lognormal models and are comparable to LIBOR market models.
---
PDF链接:
https://arxiv.org/pdf/1106.2478